Analytical approach for the approximate solution of the longitudinal structure function with respect to the GLR-MQ equation at small x

We show that the nonlinear corrections to the longitudinal structure function can be tamed the singularity behavior at low x values, with respect to GLR-MQ equations. This approach can determined the shadowing longitudinal structure function based on the shadowing corrections to the gluon and singlet quark structure functions. Comparing our results with HERA data show that at very low x this behavior completely tamed by these corrections.